Species Concentration Equations Research Articles

Radiation absorption effect on MHD natural convective flow past an impulsively started infinite vertical plate with chemical reaction and thermal radiation

AbstractThe current work is interested on investigating the impacts of thermal radiation, chemical reaction, and absorption radiation of a hydromagnetic convection‐free mass and heat transfer flow in case of an electrically conducting fluid that passes through a vertical plate moving impulsively. The analytical solutions of the governing momentum, energy, and species concentration equations with the initial and boundary conditions are obtained by the Laplace transformation technique. Graphs for fluid characteristics are used to analyze the impact of changing parametric quantities such as M, N, Sc, Kc, Q, Gr, Gm, and t on the temperature, velocity, concentration, and Sherwood number. We derive the engineering curiosity expressions for the Nusselt number and stress, and at the end, we tabulate and discuss the consequences of new parameters. The magnetic field effect and the chemical reaction are seen to diminish the fluid velocity and concentration, respectively, but in contrast, the absorption radiation effect is seen to accelerate both velocity and temperature. It is closely studied that the Nusselt number and skin friction values for hydrogen consistently exceed those for carbon monoxide.

Heat generation effects on Magnetohydrodynamic Powell-Eyring fluid flow along a vertical surface with a Chemical reaction

This work examines the influence of double diffusion on MHD Powell-Eyring fluid flow with free convection through a vertical surface. In addition, the impacts of chemical reaction, heat generation, local magnetic field, Grashof number and local modified Grashof number parameters are considered. The analysis of double diffusive in the occurrence of fluid flow under the convective surface conditions is studied. To translate the governing PDEs of velocity, energy and species (solutal) concentration equation, a couple of nonlinear ODEs we relate the suitable transformation of similarity. The set of nonlinear ODE's numerically and attained numerical consequences are connected by those gained through the assistance of MATLAB procedure bvp4c. The impact of prominent constraints of chemical reaction, Prandtl number, Schmidt number, heat source parameter, magneto hydrodynamic parameter, on dimension less velocity, energy and solutal (species) concentration dissemination has been considered. Impacts of different parameters such as skin friction coefficient, Nusselt number and Sherwood number are described through tables.

Turbulent Flame Propagation in Hydrogen-Air and Methane-Air Mixtures in the Field of Synthetic Turbulence: Direct Numerical Simulation

A technique alternative to the direct numerical simulation of turbulent combustion of gas mixtures is proposed. It is based on the solution of the three-dimensional transport equations for species concentrations and the energy conservation equation in the “synthetic” field of constant-pressure homogeneous, isotropic and statistically stationary (forced) turbulence using the detailed reaction mechanism. The synthetic turbulence with given spatial and temporal correlation functions is generated using the Monte Carlo method, assuming that the components of the vector of fluctuation velocity obey the normal Gaussian distribution. The technique is applied to the problem of turbulent combustion of fuel-lean and stoichiometric mixtures of hydrogen and methane with air at a turbulence intensity up to 10 m/s. The calculated turbulent flame propagation velocities agree satisfactorily with the values measured in the fan-stirred bomb. The predicted volume fractions of active reaction centers H, O, and OH in a turbulent flame are shown to be less than in a laminar flame up to an order of magnitude, which also agrees with the experiment. In general, calculations indicate that the “wrinkled flame” model is applicable to fuel-lean and stoichiometric mixtures of hydrogen and methane with air at turbulence intensities up to 10 m/s

Accurate Prediction of Transport Coefficients of an Evaporating Liquid Drop

Abstract Numerical simulations were carried out to study the evaporation of a drop that is released into a parallel stream of fluid at a higher temperature. A coupled level-set and volume-of-fluid (CLSVOF) interface capturing method was deployed to capture the dynamic interface between the drop liquid and the surrounding fluid. Modified forms of mass, momentum, and energy equations were solved together with the species concentration equation. The pressure jump at the interface was handled by accurate estimation of the continuum surface force. The jumps in mass and energy at the interface were carefully resolved by considering appropriate source terms in the continuity and energy equations. At the interface, the procedure of velocity computation was incorporated by extending the liquid-phase velocity onto the entire domain and by calculating the Stefan flow to predict the interface velocity accurately. The calculation of the velocity using this step leads to the exact estimation of mass transfer through the interface. The model was validated against both temperature gradient-based and vapor mass concentration gradient-based evaporation test cases. Temporal histories of the average Nusselt number and Sherwood number during the lifetime of an evaporating drop were predicted in terms of the pertinent input parameters, namely, Reynolds number, Prandtl number, and Schmidt number.

Chemical reaction, Soret and Dufour impacts on magnetohydrodynamic heat transfer Casson fluid over an exponentially permeable stretching surface with slip effects

This paper discusses the impacts of velocity, temperature, and solutal slip on the mass and heat transfer characterization of MHD mixed convection Casson fluid flow along an exponential permeable stretching surface with chemical reaction, Dufour and Soret effects. The Casson fluid is supposed to flow across an exponentially stretched sheet, together with the exponential temperature and concentration fluctuations of the fluid. As governing equations, the momentum, energy and species concentration equations are constructed and represented as PDEs. Following that, these equations were converted via the similarity transformation into ODEs. Finally, the ODEs are numerically solved using the Keller-box method with MATLAB software’s algorithm. Expressions are produced for the fluid flow, temperature and concentration gradients. We also determined the physical variables from which the friction factor, rate of mass and heat transfer are attained for engineering purposes. Using graphs and tables, the impacts of altered physical characteristics on flow amounts are explored. The consistency and validity of our outcomes revealed a significant degree of agreement when comparing them to previously published studies. The findings reveal that raising the Soret and Dufour parameter enhances the velocity profile at the wall, but the converse is true for increasing the velocity slip factor.

A generalized CFD model for evaluating catalytic separation process in structured porous materials

A hybrid multiphase model is developed to simulate the simultaneous momentum, heat and mass transfer and heterogeneous catalyzed reaction in structured catalytic porous materials. The approach relies on the combination of the volume of fluid (VOF) and Eulerian–Eulerian models, and several plug-in field functions. The VOF method is used to capture the gas–liquid interface motion, and the Eulerian–Eulerian framework solves the temperature and chemical species concentration equations for each phase. The self-defined field functions utilize a single-domain approach to overcome convergence difficulty when applying the hybrid multiphase for a multi-domain problem. The method is then applied to investigate selective removal of specific species in multicomponent reactive evaporation process. The results show that the coupling of catalytic reaction and interface species mass transfer at the phase interface is conditional, and the coupling of catalytic reaction and momentum transfer across fluid–porous interface significantly affects the conversion rate of reactants. Based on the numerical results, a strategy is proposed for matching solid catalyst with operating condition in catalytic distillation application.

Nanofluid flow in a converging and diverging channel of rectangular and heated walls

We have investigated the nanofluid flow in a converging and diverging channel of heated and inclined plane walls. The wellknown Buongiorno model has been undertaken for the transport of nanoparticles in a base fluid. The upper (lower) wall of the channel has the geometry and it is presented by an equation of the straight line y=mx+a0 (y=-mx-a0), in which m is the slope of the upper wall, a0 is the half width of the channel inlet (exit) for diverging (converging) flow, x and y are representing the Cartesian Coordinates. Note that the walls of the channel are uniformly and equally heated and the nanoparticle concentration at the walls is also constant. On the contrary, the flow problem is strictly described in Cartesian Coordinates. The problem is formulated for the upper half of the channel and later on the results are generalized for the lower half. The new observations are shown in different graphs. The four governing PD E’ s are simplified with the help of proper and appropriate similarity transformations and they constituted a system of ODE’s, whereas, it is equipped with several dimensionless parameters. Note that the convective terms in energy and concentration equations are disappeared in view of these similarity variables. The effects of all parameters are investigated on flow, heat and mass transfer characteristics. Moreover, effects of all parameters are seen on skin friction, rates of heat and mass transfer. In addition, classical models of nanofluid flow inside a converging and diverging channel in plane polar coordinates will be the special cases of the current modeled problem. Furthermore, the perturbation solution of the modeled equations is also determined for small values of the parameter. Note that slope m and Pr number are used as a perturbation parameters for the momentum equation and energy, species concentration equations and these solutions are valid for small values of all other parameters involved in the problem. In addition, exact solutions of the final ODE are also found for special ranges of parameters value. Moreover, the comparison is shown between the different solutions of the problem and classical solutions in tables and graphs. The temperature (concentration) profiles are increased (decreased) with the increasing of Nb, and Nt, however, both of them are increased with m. Moreover, the linear (non-linear) profiles of skin friction (rate of heat transfer) are decreased(increased) with the increasing of both Re (Pr,m) and m (Nb). In addition, the rate of mass transfer is increased linearly (non-linearly) against the increasing value of Nt (Pr) and Nb (Nb=Nt). Note that the temperature (concentration) profiles are effectively improved (declined) with the increase of thermophoretic forces, moreover, it is also rapidly increased (decreased) with the increase of concentration of nanoparticles (and their rapid fluctuations) in a converging and diverging channel.

A level-set model for mass transfer in bubbly flows

A level-set model is presented for simulating mass transfer or heat transfer in two-phase flows. The Navier-Stokes equations and mass transfer (or heat transfer) equation are discretized using a finite volume method on a collocated unstructured mesh, whereas a multiple marker level-set approach is used for interface capturing in bubble swarms. This method avoids the numerical coalescence of the fluid particles, whereas the mass conservation issue inherent to standard level-set methods is circumvented. Furthermore, unstructured flux-limiter schemes are used to discretize the convective term of momentum transport equation, level-set equations, and chemical species concentration equation, to avoid numerical oscillations around discontinuities, and to minimize the numerical diffusion. A convection-diffusion-reaction equation is used as a mathematical model for the chemical species mass transfer at the continuous phase. Because the mathematical analogy between dilute mass transfer and heat transfer, the same numerical model is applicable to solve both phenomena. The capabilities of this model are proved for the diffusion of chemical species from a sphere, external mass transfer in the buoyancy-driven motion of single bubbles and bubble swarms. Results are extensively validated by comparison with analytical solutions and empirical correlations from the literature.

Assessment of air flow distribution and hazardous release dispersion around a single obstacle using Reynolds-averaged Navier-Stokes equations

The flow around a cubical building, with a pollution source at the central point of the top of the cube, is studied. The Reynolds-averaged Navier-Stokes and species concentration equations are solved for Reynolds number, Re = 40,000, is based on the height of the cube. The predictions obtained with the standard, the Kato-Launder, and the low-Reynolds number k-epsilon models are examined with various wall functions for the near wall treatment of the flow. Results are compared against Martinuzzi and Tropea measurements (J. of Fluids Eng., 115, 85–92, 1993) for the flow field and against Li and Meroney (J. of Wind Eng. and Industrial Aerodynamics, 81, 333–345, 1983) experiments and Gaussian models for the concentration distribution. It is found that the present unstructured mesh model performs similarly to the structured mesh models. Results from the Kato-Launder model are closer to the experimental data for the flow patterns and contaminant distribution on the cube's roof. However, the Kato-Launder model has an over-prediction for the recirculation zone and the contaminant distribution windward of the cube. The standard k-epsilon and the low-Reynolds number k-epsilon models predict similar flow patterns and are closer to the experimental data of the cube's windward and side face.

Numerical Study of the Effects of Nanoparticles on Fuel Diffusion Combustion

The work investigates diffusion combustion of nanofuel made from the mixture of the base fuel and Al2O3 nanoparticles in a two-dimensional combustor with stationary horizontal walls. The numerical study was carried out by solving the problem governing equations including the continuity, momentum, energy and species concentration equations formulated for two-dimensional unsteady-state laminar convection using the finite volume method. The fully implicit scheme was used for the discretization in time; while upwind differencing and central differencing were used to discretize the convective and diffusive terms respectively. The results show that the values of the temperature and fuel concentration throughout the domain were higher during combustion of nanofuel than that of the base fuel only. Specifically, for flow streams at Re = 100, the addition of nanoparticles of volume fraction, φ = 0.05, enhanced the outlet average temperature of the combustor by 13% over that of ordinary fuel. Also, the wall temperature at steady state for nanofuel combustion is 7.4742 compared with 6.5897 for the base fuel. The high concentration of nanofuel is an indication of incomplete combustion which implies that more heat and higher temperature can be generated by increasing the flow stream of air.

A new compressive scheme to simulate species transfer across fluid interfaces using the Volume-Of-Fluid method

We present a new compressive scheme to simulate species transfer across fluid interfaces using the Volume-Of-Fluid method. We show that at high Péclet numbers, the standard Continuous Species Transfer (CST) generates large numerical diffusion in the phase concentration that can lead to inaccurate simulation of interface exchanges in a two-phase system. To solve this issue, the derivation of the concentration advection flux is revisited. We obtain an additional compressive term in the species concentration equation. This novel approach is labelled Compressive CST approach (C-CST). The method and the input of the compressive term are validated by comparison with analytical solutions of two-phase flow and species transport in a 1D tube. The C-CST approach reduces significantly the numerical errors. Then, the approach is used to investigate and upscale species transfer during drainage in 2D porous media.

Numerical simulation of nanocrystal synthesis in a microfluidic reactor

Modeling of continuous and controlled nanocrystal synthesis in a microfluidic reactor is presented. The population balance model that describes the nanocrystal synthesis consists of a population balance equation and a set of species concentration equations. In order to incorporate the effects of both reaction and diffusion limited growth conditions, a kinetic model with size-dependent growth and nucleation rate expressions are considered. An efficient finite element scheme based on Strang splitting that handles size-dependent particle diffusion and non-uniform growth expressions in the high dimensional population balance equation is proposed to solve the model equations. After the validation of the numerical scheme, an array of parametric studies is performed to study the effects of the flow condition and the growth environment on the nanocrystal synthesis in the microfluidic reactor. The computational results are consistent with the experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.

A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation

Improper mass conservation and spurious pressure fluctuations are considered as two serious limitations of the immersed boundary method (IBM) for modeling flow over moving/deformable bodies. Earlier attempts to overcome these issues were usually mathematically involved and computationally expensive. In one of our recent work (Kumar M, Roy S, Ali MS. An efficient immersed boundary algorithm for simulation of flows in curved and moving geometries. Comput Fluids 2016; 129: 159–178.), a simple and robust methodology is demonstrated for the sharp interface immersed boundary method which imposes proper boundary conditions for pressure and velocity in the cells intercepted by the solid boundary. In the present paper the mass conservation and pressure fluctuations of the proposed scheme are investigated in detail and the results are presented. The proposed methodology is shown not to add any computational overhead for both fixed and moving boundary problems. An overall second order accuracy is maintained in the discretization and the interpolation schemes. Validation and verification studies have been presented. The achieved results show a second order accurate mass conservation and also exhibit smooth behavior of pressure near the moving surfaces. Species concentration equation is solved to quantify the accuracy in mixing calculations. The present IBM scheme is also used to predict the terminal velocity of objects falling in a quiescent fluid medium under the actions of gravity.

Dynamics of Unsteady MHD Convective Flow with Thermophoresis of Particles and Variable Thermo-Physical Properties past a Vertical Surface Moving through Binary Mixture

The dynamics of unsteady magnetohydrodynamic convective fluid flow with radiation and thermophoresis of particles past a vertical porous plate moving through a binary mixture in an optically thin environment is investigated. The approximate form of the radiative heat flux is considered as the fourth power of temperature. Chemical reaction that occurs as the chemically reacting fluid flow through binary mixture is accounted for in energy and species concentration equations. Exponential space dependent heat source is introduced to generate additional heat energy across the fluid domain. The corresponding influence of heat energy is properly accounted for. It is assumed that viscosity and thermal conductivity vary as a linear function of temperature. The governing boundary layer equations are converted to nonlinear ordinary differential equations using similarity variables. A novel method of obtaining root finding starting with three guesses in shooting techniques is presented. The corresponding nonlinear coupled ordinary differential equations is solved numerically by shooting technique along with quadratic interpolation scheme. Graphical results of the dimensionless velocity, temperature and concentration distributions are shown for certain pertinent parameters controlling the fluid flow. The quadratic interpolation method is found to produce better estimated values of , which satisfy the degree of accuracy and proportional to the physical quantities.

Stochastic Turing patterns: analysis of compartment-based approaches.

Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter regimes, for which stochastic Turing patterns are observed, can be larger than the parameter regimes predicted by deterministic models, which are written in terms of partial differential equations (PDEs) for species concentrations. A common stochastic reaction-diffusion approach is written in terms of compartment-based (lattice-based) models, where the domain of interest is divided into artificial compartments and the number of molecules in each compartment is simulated. In this paper, the dependence of stochastic Turing patterns on the compartment size is investigated. It has previously been shown (for relatively simpler systems) that a modeler should not choose compartment sizes which are too small or too large, and that the optimal compartment size depends on the diffusion constant. Taking these results into account, we propose and study a compartment-based model of Turing patterns where each chemical species is described using a different set of compartments. It is shown that the parameter regions where spatial patterns form are different from the regions obtained by classical deterministic PDE-based models, but they are also different from the results obtained for the stochastic reaction-diffusion models which use a single set of compartments for all chemical species. In particular, it is argued that some previously reported results on the effect of noise on Turing patterns in biological systems need to be reinterpreted.

Unsteady MHD Flow of a Visco-Elastic Fluid Along Vertical Porous Surface with Chemical Reaction

An unsteady magneto hydrodynamic natural convection flow of a visco-elastic (Walters’ fluid (Model B′)) incompressible electrically conducting fluid along an infinite hot vertical porous surface with fluctuating free stream as well as suction velocity in the presence of chemical reaction has been studied. The solutions of momentum, energy, and species concentration equations under Boussinesq approximation are obtained analytically by employing successive perturbation technique. The expressions for the skin friction, Nusselt number and Sherwood number are also derived. The variations in the fluid velocity, temperature and concentration are shown graphically whereas numerical values of skin-friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters.

Heat and mass transfer on MFD flow through porous media over an accelerating surface in the presence of suction and blowing

The heat and mass transfer of electrically conducting fluid through porous media over an accelerating surface subject both to power law surface temperature and power law heat flux variations with a temperature-dependent heat source in the presence of a transverse uniform magnetic field is studied. A series solution to the energy and species concentration equation in terms of Kummer’s function is studied. The effect of Prandtl number and Schmidt number is studied with the help of graphs.

Volume of fluid method for interfacial reactive mass transfer: Application to stable liquid film

A volume of fluid method is developed in order to simulate reactive mass transfer in two-phase flows and is applied to study reactive laminar liquid film. The thermodynamic equilibrium of chemical species at the interface is considered using Henry's law. The chemical species concentration equation is solved using primitive variables and local fluxes are locally directly calculated at the interface. The present treatment of jump discontinuity of chemical concentration is consistent with a volume of fluid approach and the difficulty to calculate accurate local mass flux across interface is overcome. For plane interface, the precision of the numerical simulation is found to be very satisfactory while for curved interface a special procedure has been developed to reduce the development of spurious fluxes at the interface. The algorithm is validated for different cases by comparison with available solutions. The method is then applied to study non-reactive and reactive mass transfer in a falling liquid film. The results show that the liquid side mass transfer is well predicted by the Higbie (1935) theory when the transfer is controlled by the film advection provided that adequate parameters are considered, i.e. the actual velocity at interface and not the average liquid film velocity. For situations controlled by diffusion, the Sherwood number tends to a constant value characteristic of purely diffusive situations. For the reactive mass transfer, first and second order irreversible chemical reactions in the liquid phase are considered. The numerical results are compared respectively, with Danckwerts (1970) and Brian et al. (1961) solutions and good agreement is observed. The proposed Volume of Fluid method is shown to be well adapted to deal with interfacial reactive mass transfer problems.

An unsteady microfluidic T-form mixer perturbed by hydrodynamic pressure

An unsteady microfluidic T-form mixer driven by pressure disturbances was designed and investigated. The performance of the mixer was examined both through numerical simulation and experimentation. Linear Stokes equations were used for these low Reynolds number flows. Unsteady mixing in a micro-channel of two aqueous solutions differing in concentrations of chemical species was described using a convection-dominated diffusion equation. The task was greatly simplified by employing linear superimposition of a velocity field for solving a scalar species concentration equation. Low-order-based numerical codes were found not to be suitable for simulation of a convection-dominated mixing process due to erroneous computational dissipation. The convection-dominated diffusion problem was addressed by designing a numerical algorithm with high numerical accuracy and computational-cost effectiveness. This numerical scheme was validated by examining a test case prior to being applied to the mixing simulation. Parametric analysis was performed using this newly developed numerical algorithm to determine the best mixing conditions. Numerical simulation identified the best mixing condition to have a Strouhal number (St) of 0.42. For a T-junction mixer (with channel width = 196 µm), about 75% mixing can be finished within a mixing distance of less than 3 mm (i.e. 15 channel width) at St = 0.42 for flow with a Reynolds number less than 0.24. Numerical results were validated experimentally by mixing two aqueous solutions containing yellow and blue dyes. Visualization of the flow field under the microscope revealed a high level of agreement between numerical simulation and experimental results.

Numerical study of double-diffusive, free convective flow past a moving vertical cylinder

The double-diffusive, free convective flow past a moving semi-infinite vertical cylinder has been studied numerically. The mass, momentum, energy, and species concentration equations have been solved by a finite-difference method using an implicit scheme of Crank-Nicolson type. The finite-difference scheme is unconditionally stable and accurate. Graphical results for the velocity, temperature, concentration, local and average skin friction, and Nusselt and Sherwood numbers are illustrated and discussed for various physical parametric values. The role of temperature stratification in the ambient medium has been analyzed.